We present a first-principles study of the energy and elastic properties of solid helium at pressures below the range in which it is energetically stable. We find that the limit of mechanical stability in hcp He is bar, which lies significantly below the spinodal pressure found in the liquid phase (i.e., bar). Furthermore, we show that the pressure variation of the transverse and longitudinal sound velocities close to does not follow a power law of the form , in contrast to what is observed in the fluid.